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Journal articles on the topic 'Implicit regularization'

Author: Grafiati

Published: 30 November 2024

Last updated: 31 July 2025

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1

Ceng, Lu-Chuan, Qamrul Hasan Ansari, and Ching-Feng Wen. "Implicit Relaxed and Hybrid Methods with Regularization for Minimization Problems and Asymptotically Strict Pseudocontractive Mappings in the Intermediate Sense." Abstract and Applied Analysis 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/854297.

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We first introduce an implicit relaxed method with regularization for finding a common element of the set of fixed points of an asymptotically strict pseudocontractive mappingSin the intermediate sense and the set of solutions of the minimization problem (MP) for a convex and continuously Frechet differentiable functional in the setting of Hilbert spaces. The implicit relaxed method with regularization is based on three well-known methods: the extragradient method, viscosity approximation method, and gradient projection algorithm with regularization. We derive a weak convergence theorem for tw

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2

Klädtke, Manuel, and Moritz Schulze Darup. "Towards explainable data-driven predictive control with regularizations." at - Automatisierungstechnik 73, no. 6 (2025): 365–82. https://doi.org/10.1515/auto-2024-0161.

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Abstract Data-driven predictive control (DPC), using linear combinations of recorded trajectory data, has recently emerged as a popular alternative to traditional model predictive control (MPC). Without an explicitly enforced prediction model, the effects of commonly used regularization terms – and the resulting predictions – can be opaque. This opacity may lead to practical challenges, such as reliance on empirical tuning of regularization parameters based on closed-loop performance, and potentially misleading heuristic interpretations of norm-based regularizations. However, by examining the

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FARGNOLI, H. G., A. P. BAÊTA SCARPELLI, L. C. T. BRITO, et al. "ULTRAVIOLET AND INFRARED DIVERGENCES IN IMPLICIT REGULARIZATION: A CONSISTENT APPROACH." Modern Physics Letters A 26, no. 04 (2011): 289–302. http://dx.doi.org/10.1142/s0217732311034773.

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Implicit Regularization is a four-dimensional regularization initially conceived to treat ultraviolet divergences. It has been successfully tested in several instances in the literature, more specifically in those where Dimensional Regularization does not apply. In the present contribution, we extend the method to handle infrared divergences as well. We show that the essential steps which rendered Implicit Regularization adequate in the case of ultraviolet divergences have their counterpart for infrared ones. Moreover, we show that a new scale appears, typically an infrared scale which is comp

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Sampaio, Marcos, A. P. Baêta Scarpelli, J. E. Ottoni, and M. C. Nemes. "Implicit Regularization and Renormalization of QCD." International Journal of Theoretical Physics 45, no. 2 (2006): 436–57. http://dx.doi.org/10.1007/s10773-006-9045-z.

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Al-Tam, Faroq, António dos Anjos, and Hamid Reza Shahbazkia. "Iterative illumination correction with implicit regularization." Signal, Image and Video Processing 10, no. 5 (2015): 967–74. http://dx.doi.org/10.1007/s11760-015-0847-4.

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Dandi, Yatin, Luis Barba, and Martin Jaggi. "Implicit Gradient Alignment in Distributed and Federated Learning." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 6 (2022): 6454–62. http://dx.doi.org/10.1609/aaai.v36i6.20597.

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A major obstacle to achieving global convergence in distributed and federated learning is the misalignment of gradients across clients or mini-batches due to heterogeneity and stochasticity of the distributed data. In this work, we show that data heterogeneity can in fact be exploited to improve generalization performance through implicit regularization. One way to alleviate the effects of heterogeneity is to encourage the alignment of gradients across different clients throughout training. Our analysis reveals that this goal can be accomplished by utilizing the right optimization method that

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Rosado, R. J. C., A. Cherchiglia, M. Sampaio, and B. Hiller. "An Implicit Regularization Approach to Chiral Models." Acta Physica Polonica B Proceedings Supplement 17, no. 6 (2024): 1. http://dx.doi.org/10.5506/aphyspolbsupp.17.6-a15.

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8

Liu, Yuan, Yanzhi Song, Zhouwang Yang, and Jiansong Deng. "Implicit surface reconstruction with total variation regularization." Computer Aided Geometric Design 52-53 (March 2017): 135–53. http://dx.doi.org/10.1016/j.cagd.2017.02.005.

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Li, Zhemin, Tao Sun, Hongxia Wang, and Bao Wang. "Adaptive and Implicit Regularization for Matrix Completion." SIAM Journal on Imaging Sciences 15, no. 4 (2022): 2000–2022. http://dx.doi.org/10.1137/22m1489228.

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10

Belytschko, T., S. P. Xiao, and C. Parimi. "Topology optimization with implicit functions and regularization." International Journal for Numerical Methods in Engineering 57, no. 8 (2003): 1177–96. http://dx.doi.org/10.1002/nme.824.

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11

Lin, Huangxing, Yihong Zhuang, Xinghao Ding, et al. "Self-Supervised Image Denoising Using Implicit Deep Denoiser Prior." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 2 (2023): 1586–94. http://dx.doi.org/10.1609/aaai.v37i2.25245.

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We devise a new regularization for denoising with self-supervised learning. The regularization uses a deep image prior learned by the network, rather than a traditional predefined prior. Specifically, we treat the output of the network as a ``prior'' that we again denoise after ``re-noising.'' The network is updated to minimize the discrepancy between the twice-denoised image and its prior. We demonstrate that this regularization enables the network to learn to denoise even if it has not seen any clean images. The effectiveness of our method is based on the fact that CNNs naturally tend to cap

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12

Arias-Perdomo, Dafne Carolina, Adriano Cherchiglia, Brigitte Hiller, and Marcos Sampaio. "A Brief Review of Implicit Regularization and Its Connection with the BPHZ Theorem." Symmetry 13, no. 6 (2021): 956. http://dx.doi.org/10.3390/sym13060956.

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Quantum Field Theory, as the keystone of particle physics, has offered great insights into deciphering the core of Nature. Despite its striking success, by adhering to local interactions, Quantum Field Theory suffers from the appearance of divergent quantities in intermediary steps of the calculation, which encompasses the need for some regularization/renormalization prescription. As an alternative to traditional methods, based on the analytic extension of space–time dimension, frameworks that stay in the physical dimension have emerged; Implicit Regularization is one among them. We briefly re

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Zhang, Zhe, and Xiaoyang Tan. "An Implicit Trust Region Approach to Behavior Regularized Offline Reinforcement Learning." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 15 (2024): 16944–52. http://dx.doi.org/10.1609/aaai.v38i15.29637.

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We revisit behavior regularization, a popular approach to mitigate the extrapolation error in offline reinforcement learning (RL), showing that current behavior regularization may suffer from unstable learning and hinder policy improvement. Motivated by this, a novel reward shaping-based behavior regularization method is proposed, where the log-probability ratio between the learned policy and the behavior policy is monitored during learning. We show that this is equivalent to an implicit but computationally lightweight trust region mechanism, which is beneficial to mitigate the influence of es

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14

Dias, E. W., A. P. Baêta Scarpelli, L. C. T. Brito, and H. G. Fargnoli. "Multiloop calculations with implicit regularization in massless theories." Brazilian Journal of Physics 40, no. 2 (2010): 228–34. http://dx.doi.org/10.1590/s0103-97332010000200018.

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15

Karageorgos, Konstantinos, Anastasios Dimou, Federico Alvarez, and Petros Daras. "Implicit and Explicit Regularization for Optical Flow Estimation." Sensors 20, no. 14 (2020): 3855. http://dx.doi.org/10.3390/s20143855.

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In this paper, two novel and practical regularizing methods are proposed to improve existing neural network architectures for monocular optical flow estimation. The proposed methods aim to alleviate deficiencies of current methods, such as flow leakage across objects and motion consistency within rigid objects, by exploiting contextual information. More specifically, the first regularization method utilizes semantic information during the training process to explicitly regularize the produced optical flow field. The novelty of this method lies in the use of semantic segmentation masks to teach

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Scolnik, H. D., N. E. Echebest, and M. T. Guardarucci. "Implicit regularization of the incomplete oblique projections method." International Transactions in Operational Research 16, no. 4 (2009): 525–46. http://dx.doi.org/10.1111/j.1475-3995.2009.00694.x.

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17

Wang, Li, Zhiguo Fu, Yingcong Zhou, and Zili Yan. "The Implicit Regularization of Momentum Gradient Descent in Overparametrized Models." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 8 (2023): 10149–56. http://dx.doi.org/10.1609/aaai.v37i8.26209.

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The study of the implicit regularization induced by gradient-based optimization in deep learning is a long-standing pursuit. In the present paper, we characterize the implicit regularization of momentum gradient descent (MGD) in the continuous-time view, so-called momentum gradient flow (MGF). We show that the components of weight vector are learned for a deep linear neural networks at different evolution rates, and this evolution gap increases with the depth. Firstly, we show that if the depth equals one, the evolution gap between the weight vector components is linear, which is consistent wi

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Arruda, M. R. T., M. Trombini, and A. Pagani. "Implicit to Explicit Algorithm for ABAQUS Standard User-Subroutine UMAT for a 3D Hashin-Based Orthotropic Damage Model." Applied Sciences 13, no. 2 (2023): 1155. http://dx.doi.org/10.3390/app13021155.

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This study examines a new approach to facilitate the convergence of upcoming user-subroutines UMAT when the secant material matrix is applied rather than the conventional tangent (also known as Jacobian) material matrix. This algorithm makes use of the viscous regularization technique to stabilize the numerical solution of softening material models. The Newton–Raphson algorithm predictor-corrector of ABAQUS then applies this type of viscous regularization to a UMAT using only the secant matrix. When the time step is smaller than the viscosity parameter, this type of regularization may be unsui

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Plusch, Grigoriy, Sergey Arsenyev-Obraztsov, and Olga Kochueva. "The Weights Reset Technique for Deep Neural Networks Implicit Regularization." Computation 11, no. 8 (2023): 148. http://dx.doi.org/10.3390/computation11080148.

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We present a new regularization method called Weights Reset, which includes periodically resetting a random portion of layer weights during the training process using predefined probability distributions. This technique was applied and tested on several popular classification datasets, Caltech-101, CIFAR-100 and Imagenette. We compare these results with other traditional regularization methods. The subsequent test results demonstrate that the Weights Reset method is competitive, achieving the best performance on Imagenette dataset and the challenging and unbalanced Caltech-101 dataset. This me

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Lyu, Bochen, He Wang, Zheng Wang, and Zhanxing Zhu. "Effects of Momentum in Implicit Bias of Gradient Flow for Diagonal Linear Networks." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 18 (2025): 19242–50. https://doi.org/10.1609/aaai.v39i18.34118.

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This paper targets on the regularization effect of momentum-based methods in regression settings and analyzes the popular diagonal linear networks to precisely characterize the implicit bias of continuous versions of heavy-ball (HB) and Nesterov's method of accelerated gradients (NAG). We show that, HB and NAG exhibit different implicit bias compared to GD for diagonal linear networks, which is different from the one for classic linear regression problem where momentum-based methods share the same implicit bias with GD. Specifically, the role of momentum in the implicit bias of GD is twofold:

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21

Dubikovsky, A. I., and P. K. Silaev. "On an alternative, implicit renormalization procedure for the Casimir energy." Modern Physics Letters A 33, no. 22 (2018): 1850129. http://dx.doi.org/10.1142/s0217732318501298.

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We propose a procedure for the renormalization of Casimir energy that is based on the implicit versions of standard steps of renormalization procedure — regularization, subtraction and removing the regularization. The proposed procedure is based on the calculation of a set of convergent sums, which are related to the original divergent sum for the non-renormalized Casimir energy. Then, we construct a linear equation system that connects this set of convergent sums with the renormalized Casimir energy, which is a solution to this system of equations. This procedure slightly reduces the indeterm

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22

Fanuel, Michael, Joachim Schreurs, and Johan Suykens. "Diversity Sampling is an Implicit Regularization for Kernel Methods." SIAM Journal on Mathematics of Data Science 3, no. 1 (2021): 280–97. http://dx.doi.org/10.1137/20m1320031.

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23

Pontes, Carlos R., A. P. Baêta Scarpelli, Marcos Sampaio, and M. C. Nemes. "Implicit regularization beyond one-loop order: scalar field theories." Journal of Physics G: Nuclear and Particle Physics 34, no. 10 (2007): 2215–34. http://dx.doi.org/10.1088/0954-3899/34/10/011.

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24

Dias, E. W., A. P. Baêta Scarpelli, L. C. T. Brito, M. Sampaio, and M. C. Nemes. "Implicit regularization beyond one-loop order: gauge field theories." European Physical Journal C 55, no. 4 (2008): 667–81. http://dx.doi.org/10.1140/epjc/s10052-008-0614-6.

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25

CHERCHIGLIA, A. L., MARCOS SAMPAIO, and M. C. NEMES. "SYSTEMATIC IMPLEMENTATION OF IMPLICIT REGULARIZATION FOR MULTILOOP FEYNMAN DIAGRAMS." International Journal of Modern Physics A 26, no. 15 (2011): 2591–635. http://dx.doi.org/10.1142/s0217751x11053419.

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Implicit Regularization (IReg) is a candidate to become an invariant framework in momentum space to perform Feynman diagram calculations to arbitrary loop order. In this work we present a systematic implementation of our method that automatically displays the terms to be subtracted by Bogoliubov's recursion formula. Therefore, we achieve a twofold objective: we show that the IReg program respects unitarity, locality and Lorentz invariance and we show that our method is consistent since we are able to display the divergent content of a multiloop amplitude in a well-defined set of basic divergen

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26

Tian, Ming, and Jun-Ying Gong. "Strong Convergence of Modified Algorithms Based on the Regularization for the Constrained Convex Minimization Problem." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/870102.

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As is known, the regularization method plays an important role in solving constrained convex minimization problems. Based on the idea of regularization, implicit and explicit iterative algorithms are proposed in this paper and the sequences generated by the algorithms can converge strongly to a solution of the constrained convex minimization problem, which also solves a certain variational inequality. As an application, we also apply the algorithm to solve the split feasibility problem.

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27

Kim, Woosung, Donghyeon Ki, and Byung-Jun Lee. "Relaxed Stationary Distribution Correction Estimation for Improved Offline Policy Optimization." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 12 (2024): 13185–92. http://dx.doi.org/10.1609/aaai.v38i12.29218.

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One of the major challenges of offline reinforcement learning (RL) is dealing with distribution shifts that stem from the mismatch between the trained policy and the data collection policy. Stationary distribution correction estimation algorithms (DICE) have addressed this issue by regularizing the policy optimization with f-divergence between the state-action visitation distributions of the data collection policy and the optimized policy. While such regularization naturally integrates to derive an objective to get optimal state-action visitation, such an implicit policy optimization framework

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Hilali, Youssef, Bouazza Braikat, Hassane Lahmam, and Noureddine Damil. "An implicit algorithm for the dynamic study of nonlinear vibration of spur gear system with backlash." Mechanics & Industry 19, no. 3 (2018): 310. http://dx.doi.org/10.1051/meca/2017006.

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In this work, we propose some regularization techniques to adapt the implicit high order algorithm based on the coupling of the asymptotic numerical methods (ANM) (Cochelin et al., Méthode Asymptotique Numérique, Hermès-Lavoisier, Paris, 2007; Mottaqui et al., Comput. Methods Appl. Mech. Eng. 199 (2010) 1701–1709; Mottaqui et al., Math. Model. Nat. Phenom. 5 (2010) 16–22) and the implicit Newmark scheme for solving the non-linear problem of dynamic model of a two-stage spur gear system with backlash. The regularization technique is used to overcome the numerical difficulties of singularities e

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Zhang, Meng, Jiaxin Li, Chengcheng Yang, and Quan Chen. "Deflated Restarting of Exponential Integrator Method with an Implicit Regularization for Efficient Transient Circuit Simulation." Electronics 10, no. 9 (2021): 1124. http://dx.doi.org/10.3390/electronics10091124.

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Exponential integrator (EI) method based on Krylov subspace approximation is a promising method for large-scale transient circuit simulation. However, it suffers from the singularity problem and consumes large subspace dimensions for stiff circuits when using the ordinary Krylov subspace. Restarting schemes are commonly applied to reduce the subspace dimension, but they also slow down the convergence and degrade the overall computational efficiency. In this paper, we first devise an implicit and sparsity-preserving regularization technique to tackle the singularity problem facing EI in the ord

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Pontes, C. R., A. P. Baêta Scarpelli, Marcos Sampaio, J. L. Acebal, and M. C. Nemes. "On the equivalence between implicit regularization and constrained differential renormalization." European Physical Journal C 53, no. 1 (2007): 121–31. http://dx.doi.org/10.1140/epjc/s10052-007-0437-x.

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31

Zreid, Imadeddin, and Michael Kaliske. "Regularization of microplane damage models using an implicit gradient enhancement." International Journal of Solids and Structures 51, no. 19-20 (2014): 3480–89. http://dx.doi.org/10.1016/j.ijsolstr.2014.06.020.

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32

Laurent, Gautier. "Iterative Thickness Regularization of Stratigraphic Layers in Discrete Implicit Modeling." Mathematical Geosciences 48, no. 7 (2016): 811–33. http://dx.doi.org/10.1007/s11004-016-9637-y.

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33

Mohsin, Yasir Q., Sajan Goud Lingala, Edward DiBella, and Mathews Jacob. "Accelerated dynamic MRI using patch regularization for implicit motion compensation." Magnetic Resonance in Medicine 77, no. 3 (2016): 1238–48. http://dx.doi.org/10.1002/mrm.26215.

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34

Zheng, Bin, Junfeng Liu, Zhenyu Zhao, Zhihong Dou, and Benxue Gong. "A Generalized Iterated Tikhonov Method in the Fourier Domain for Determining the Unknown Source of the Time-Fractional Diffusion Equation." Symmetry 16, no. 7 (2024): 864. http://dx.doi.org/10.3390/sym16070864.

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In this paper, an inverse problem of determining a source in a time-fractional diffusion equation is investigated. A Fourier extension scheme is used to approximate the solution to avoid the impact on smoothness caused by directly using singular system eigenfunctions for approximation. A modified implicit iteration method is proposed as a regularization technique to stabilize the solution process. The convergence rates are derived when a discrepancy principle serves as the principle for choosing the regularization parameters. Numerical tests are provided to further verify the efficacy of the p

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Sneha, U., and Samuel Liji. "Survey on Users Ranking Pattern based Trust Model Regularization in Product Recommendation." International Journal of Trend in Scientific Research and Development 2, no. 3 (2018): 1859–71. https://doi.org/10.31142/ijtsrd11302.

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It is recommended to trust SVD, a trust based matrix decomposition technique to provide advice. Trust SVD is integrated into the recommendation model to reduce data sparsity and cold start issues and their recommended performance degradation. The proposed system is a new framework for social trust data from four real world datasets, which indicates that not only the explicit and implicit impact of ratings and trust should be considered in the recommendation model. Trust SVD extends to SVD , using the explicit and implicit impact of rated projects by further combining the explicit and implicit

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Zhao, Jiajia, and Zuoliang Xu. "Calibration of time-dependent volatility for European options under the fractional Vasicek model." AIMS Mathematics 7, no. 6 (2022): 11053–69. http://dx.doi.org/10.3934/math.2022617.

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<abstract><p>In this paper, we calibrate the time-dependent volatility function for European options under the fractional Vasicek interest rate model. A fully implicit finite difference method is applied to solve the partial differential equation of option pricing numerically. To find the volatility function, we minimize a cost function that is the sum of the squared errors between the theoretical prices and market prices with Tikhonov $ L_2 $ regularization and $ L_{1/2} $ regularization respectively. Finally numerical experiments with simulated and real market data verify the eff

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Reshniak, Viktor, and Clayton G. Webster. "Robust Learning with Implicit Residual Networks." Machine Learning and Knowledge Extraction 3, no. 1 (2020): 34–55. http://dx.doi.org/10.3390/make3010003.

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In this effort, we propose a new deep architecture utilizing residual blocks inspired by implicit discretization schemes. As opposed to the standard feed-forward networks, the outputs of the proposed implicit residual blocks are defined as the fixed points of the appropriately chosen nonlinear transformations. We show that this choice leads to the improved stability of both forward and backward propagations, has a favorable impact on the generalization power, and allows for control the robustness of the network with only a few hyperparameters. In addition, the proposed reformulation of ResNet

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Guo, Minghao, and Yan Gao. "Adaptive Approximate Implicitization of Planar Parametric Curves via Asymmetric Gradient Constraints." Symmetry 15, no. 9 (2023): 1738. http://dx.doi.org/10.3390/sym15091738.

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Converting a parametric curve into the implicit form, which is called implicitization, has always been a popular but challenging problem in geometric modeling and related applications. However, existing methods mostly suffer from the problems of maintaining geometric features and choosing a reasonable implicit degree. The present paper has two contributions. We first introduce a new regularization constraint (called the asymmetric gradient constraint) for both polynomial and non-polynomial curves, which efficiently possesses shape-preserving. We then propose two adaptive algorithms of approxim

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Tan, Zhaorui, Xi Yang, and Kaizhu Huang. "Semantic-Aware Data Augmentation for Text-to-Image Synthesis." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 6 (2024): 5098–107. http://dx.doi.org/10.1609/aaai.v38i6.28315.

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Data augmentation has been recently leveraged as an effective regularizer in various vision-language deep neural networks. However, in text-to-image synthesis (T2Isyn), current augmentation wisdom still suffers from the semantic mismatch between augmented paired data. Even worse, semantic collapse may occur when generated images are less semantically constrained. In this paper, we develop a novel Semantic-aware Data Augmentation (SADA) framework dedicated to T2Isyn. In particular, we propose to augment texts in the semantic space via an Implicit Textual Semantic Preserving Augmentation, in con

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Hu, Wei. "Understanding Surprising Generalization Phenomena in Deep Learning." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 20 (2024): 22669. http://dx.doi.org/10.1609/aaai.v38i20.30285.

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Deep learning has exhibited a number of surprising generalization phenomena that are not captured by classical statistical learning theory. This talk will survey some of my work on the theoretical characterizations of several such intriguing phenomena: (1) Implicit regularization: A major mystery in deep learning is that deep neural networks can often generalize well despite their excessive expressive capacity. Towards explaining this mystery, it has been suggested that commonly used gradient-based optimization algorithms enforce certain implicit regularization which effectively constrains the

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41

Gobira, S. R., and M. C. Nemes. "N-Loop Treatment of Overlapping Diagrams by the Implicit Regularization Technique." International Journal of Theoretical Physics 42, no. 11 (2003): 2765–95. http://dx.doi.org/10.1023/b:ijtp.0000005983.70240.34.

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Zhu, Yulian, Songcan Chen, and Qing Tian. "Spatial regularization in subspace learning for face recognition: implicit vs. explicit." Neurocomputing 173 (January 2016): 1554–64. http://dx.doi.org/10.1016/j.neucom.2015.09.028.

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43

Ottoni, J. E., A. P. Baêta Scarpelli, Marcos Sampaio, and M. C. Nemes. "Supergravity corrections to the (g−2)l factor by implicit regularization." Physics Letters B 642, no. 3 (2006): 253–62. http://dx.doi.org/10.1016/j.physletb.2006.09.025.

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Kim, Hyungmin, Sungho Suh, Sunghyun Baek, et al. "AI-KD: Adversarial learning and Implicit regularization for self-Knowledge Distillation." Knowledge-Based Systems 293 (June 2024): 111692. http://dx.doi.org/10.1016/j.knosys.2024.111692.

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45

Yuldashev, T. K., Z. K. Eshkuvatov, and N. M. A. Nik Long. "Nonlinear the first kind Fredholm integro-differential first-order equation with degenerate kernel and nonlinear maxima." Mathematical Modeling and Computing 9, no. 1 (2022): 74–82. http://dx.doi.org/10.23939/mmc2022.01.074.

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In this note, the problems of solvability and construction of solutions for a nonlinear Fredholm one-order integro-differential equation with degenerate kernel and nonlinear maxima are considered. Using the method of degenerate kernel combined with the method of regularization, we obtain an implicit the first-order functional-differential equation with the nonlinear maxima. Initial boundary conditions are used to ensure the solution uniqueness. In order to use the method of a successive approximations and prove the one value solvability, the obtained implicit functional-differential equation i

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Liu, Jiangxin, Lijian Wu, Kexin Yin, Changjun Song, Xiaolin Bian, and Shengting Li. "Methods for Solving Finite Element Mesh-Dependency Problems in Geotechnical Engineering—A Review." Sustainability 14, no. 5 (2022): 2982. http://dx.doi.org/10.3390/su14052982.

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The instabilities of soil specimens in laboratory or soil made geotechnical structures in field are always numerically simulated by the classical continuum mechanics-based constitutive models with finite element method. However, finite element mesh dependency problems are inevitably encountered when the strain localized failure occurs especially in the post-bifurcation regime. In this paper, an attempt is made to summarize several main numerical regularization techniques used in alleviating the mesh dependency problems, i.e., viscosity theory, nonlocal theory, high-order gradient and micropola

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Lin Cui, Lin Cui, Caiyin Wang Lin Cui, Zhiwei Zhang Caiyin Wang, Xiaoyong Yu Zhiwei Zhang, and Fanghui Zha Xiaoyong Yu. "Fusing Dual Geo-Social Relationship and Deep Implicit Interest Topic Similarity for POI Recommendation." 網際網路技術學刊 23, no. 4 (2022): 791–99. http://dx.doi.org/10.53106/160792642022072304014.

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<p>Nowadays, POI recommendation has been a hot research area, which are almost based on incomplete social relationships and geographical influence. However, few research simultaneously focuses on the refined social relationship and the user deep implicit topic similarity under a reachable region. Under this background, a novel Dual Geo-Social Relationship and Deep Implicit Interest Topic Similarity mining under a Reachable Region for POI Recommendation (DDR-PR) is proposed. DDR-PR first adopts kernel density estimation to compute the user checking-in reachable area. Under the reachable a

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Badriev, I. B., O. A. Zadvornov, and L. N. Ismagilov. "On Iterative Regularization Methods for Variational Inequalities of the Second Kind with Pseudomonotone Operators." Computational Methods in Applied Mathematics 3, no. 2 (2003): 223–34. http://dx.doi.org/10.2478/cmam-2003-0015.

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Iqbal, Sajad, and Yujie Wei. "Recovery of the time-dependent implied volatility of time fractional Black–Scholes equation using linearization technique." Journal of Inverse and Ill-posed Problems 29, no. 4 (2021): 599–610. http://dx.doi.org/10.1515/jiip-2020-0105.

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Abstract This paper tries to examine the recovery of the time-dependent implied volatility coefficient from market prices of options for the time fractional Black–Scholes equation (TFBSM) with double barriers option. We apply the linearization technique and transform the direct problem into an inverse source problem. Resultantly, we get a Volterra integral equation for the unknown linear functional, which is then solved by the regularization method. We use L 1 {L_{1}} -forward difference implicit approximation for the forward problem. Numerical results using L 1 {L_{1}} -forward difference imp

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Arthern, Robert J. "Exploring the use of transformation group priors and the method of maximum relative entropy for Bayesian glaciological inversions." Journal of Glaciology 61, no. 229 (2015): 947–62. http://dx.doi.org/10.3189/2015jog15j050.

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AbstractIce-sheet models can be used to forecast ice losses from Antarctica and Greenland, but to fully quantify the risks associated with sea-level rise, probabilistic forecasts are needed. These require estimates of the probability density function (PDF) for various model parameters (e.g. the basal drag coefficient and ice viscosity). To infer such parameters from satellite observations it is common to use inverse methods. Two related approaches are in use: (1) minimization of a cost function that describes the misfit to the observations, often accompanied by explicit or implicit regularizat

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